vs. ?

While reading [1] Bertrand Russell’s History of Western Philosophy the above picture occured to me and I decided to write here some comments on Ockham’s razor and its possible usefulness to modern physics. Bellow you’ll find some lines which you might enjoy (explicitly, I just mention modern physics issues a couple of times, perhaps in the future I’ll write more). Paraphrasing a Siegel’s parody blog, if this post were really serious, it would not be here, it would be published elsewhere. :-)

The first time I heard about Ockham’s razor (aka, Occam’s razor), about 10 years ago, I thought it was a strong principle with a leading role in science. Curiously for me by then, “serious” philosophy of science books seldom mention Ockham’s razor, it appears it’s frequently cited and used only in “soft” books on philosophy of science or science divulgation. Some years later and until recently, it became clear to me that Ockham’s razor was completely useless. However, as now I understand, Ockham’s original statements were relevant to the establishment of modern science and, in a certain sense, they’re still important to science. As a criterion to decide what is the best explanation or theory, nonetheless, I still think it’s useless. I think Ockham’s razor is blunt, although his original statements are not.

Some history: William of Ockham. William of Ockham (~1290 – 1349 a.D.) was a Franciscan born in Ockham, a village in Surrey, England. Ockham had a different view on the role of faith and reason than the advocated by the Catholic Church of his time [which, as far as I understand, was inclined to St. Thomas Aquinas's philosophy, who brought Aristotle's metaphysics to the Catholic Church and had demonstrated the existence of God through 5 different ways(1)]; consequently Ockham was excommunicated in 1328 by pope John XXII. In accordance with [1], Ockham proposed that “The reality is inherent to individual things, and only these can be object of experience, leading to a direct and correct knowledge. It means that, for an explanation of the being, the complex features of Aristotle’s metaphysics was completely superfluous. It is in this sense that we should interpret Ockham’s statement that “it is useless to do with more what can be done with less”“.

From Ockham’s viewpoint, it was nonsense to use reason to justify what concerns faith and God. For him, faith should not be restricted by logical judgments, and nor philosophy nor science are restricted by faith. If I understand his point, for him faith concerns the ultimate truth, while reason the apparent, the “effective”, truth in the secular world given by our ordinary perceptions. This puts a sharp difference between the matters of faith and the matters of reason, difference which was, and still is, influent to the comprehension of science and religion.

The Razor. Ockham’s principle of exclusion of the necessity of metaphysics or teology in order to study Nature has lead to many similar, but stronger, expressions. These versions are commonly grouped under the unique name of “Ockham’s Razor” and have in common a certain quest for simplicity. Some of these Ockham’s Razor expressions have become quite popular in the context of science divulgation, e.g.,

i) Entities should not be multiplied beyond necessity;
ii) The simplest answer is usually the correct answer;
iii) Of two equivalent theories or explanations, all other things being equal, the simpler one is to be preferred.

The third one, I think, is the most “sharp” and commonly found formulation of Ockham’s razor. At least a priori, it appears to be a good principle to select one scientific theory among many others which are in practice equivalent.

How to cut with the razor? Well, in principle is very simple: given two different theories which describes some Nature’s aspect equally well (from the perspective of possible physical experiments), if one can be regarded as simpler than the other, then the more complex is eliminated, cut, in favor of simplicity. Classical examples of the application of this razor in science include the victory of the heliocentric model over the geocentric one and the establishment of special relativity with the subsequent abandon of the aether hypothesis.

I think this principle casts 3 major difficulties: i) what precisely means “two different theories or explanations” which are equivalent? ii) can something be absolutely simple? At least in principle, nothing is simple by itself, something is simple in regard to a certain criterion, so what is the criterion? iii) what’s the meaning of “cutting” the more complex explanation? Are we getting closer to the truth? Or is it just a pragmatical move, that is, is it done just to simplify conceptual or technical manipulation? Why the necessity of cutting, can’t we use both theories?

I will not try to answer above questions, I would need much more time. In particular, the last question of item iii) and the item i) may seem very easy to answer (e.g., i) different models which foresees the same experimental output; iii-last) yes, can, but since they’re equivalent it’s waste of time), but depending on the interpretation of the Ockham’s razor, I think these questions can be very problematic. For instance, in modern physics the concept of duality plays a major role (it’s essential to string theory, while it’s very useful to quantum field theory/particle physics) and duality does exactly this: connects two different “mathematical” descriptions which have the same physical content. Depending on the criterion adopted to establish the scale of simplicity, one of these dual theories may be seen as simpler than the other. Nevertheless, in physics, while dealing with duality issues, we don’t discard one description in favor of the other, we use both! Both have the same physical content, but, depending on what is being studied, one is more suitable (i.e., easy to manipulate) than the other.

Two classifications.. The Wikipedia’s article on the Ockham’s razor uses a distinction very interesting between two kind of applications: one is similar to William of Ockham’s original statements, being called ontological application, while the other is the inter-theoretic competition, which is closer to the Ockham’s Razor definition present above and in “soft” books. The first application is frequently used: one should not care about a metaphysical statements while doing science (2), science is about what we can perceive using our ordinary senses (directly or not), moreover science is capable of achieving its own truths. See the B. Russell’s citation in the begining of this post. On the other hand, the last application, concerning theory competition, is very problematic, as above vaguely pointed. If one is concerned with theory competition or development of science, I think one should look for the “hard” books on philosophy of science and forget about Ockham’s razor. In this sense, I think, Ockham’s razor is not a good vague principle related to science, it’s indeed useless.

Well, these were mine loose thoughts on Ockham’s razor. Wikipedia has a lengthy text on the subject with many external links. I need to get back to my thesis’ writing now. Comments are welcome. :-)

(1) I don’t know any site about these demonstrations, but one of them is really short and funn…, I mean, interesting. It starts with the assumption that in our world we can find things with different degrees of perfection [a rather dubious start], therefore there MUST be something completelly perfect, which is God [clearly, St. Thomas Aquinas was a not a great mathematician].
(2) To avoid an ingenuous positivism some subtleties need to be clarified, but I’ll not enter in the details here, perhaps in the future.

Hoje finalmente comprei um novo pente de memória RAM, gastei um dinheiro extra mas parece que ao menos não serei mais importunado por travamentos do sistema. Troquei meu pente de 256MB DDR400 genérico por um 512MB DDR400 Kingston. Por sinal essas memórias de marca estão hoje em dia com preços bem próximos das genéricas ou de marcas pouco recomendadas.

Verifiquei meus e-mails e encontrei uma notícia muito boa. Certo artigo meu hep-th/0603027 está com dificuldades de ser publicado por ter um resultado conflitante com uma proposição de hep-th/0210171. Após muita revisão de conta, tudo indicava, sob nosso ponto de vista, que o nosso trabalho estava correto e a proposição deles tinha algum problema. Hoje recebi o e-mail de resposta do outro grupo de pesquisa (há algum tempo enviei um e-mail para eles a fim de estarem cientes do conflito). Na resposta era admitido que a proposição deles possui algum problema. Sou muito grato a eles pela cordial resposta. O artigo hep-th/0210171 trata de aspectos gerais do eletromagnetismo não-comutativo, incluindo algumas análises numéricas e, estando nosso artigo correto, só precisa da hipótese extra de que os campos variam lentamente no tempo e no espaço (hipótese natural, devido à conexão com teoria de cordas) [hep-th/9908142, hep-th/0404064].

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